3.1360 \(\int (1-2 x)^3 (2+3 x)^2 (3+5 x)^3 \, dx\)

Optimal. Leaf size=67 \[ \frac{125}{64} (1-2 x)^9-\frac{12675}{512} (1-2 x)^8+\frac{28555}{224} (1-2 x)^7-\frac{21439}{64} (1-2 x)^6+\frac{144837}{320} (1-2 x)^5-\frac{65219}{256} (1-2 x)^4 \]

[Out]

(-65219*(1 - 2*x)^4)/256 + (144837*(1 - 2*x)^5)/320 - (21439*(1 - 2*x)^6)/64 + (
28555*(1 - 2*x)^7)/224 - (12675*(1 - 2*x)^8)/512 + (125*(1 - 2*x)^9)/64

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Rubi [A]  time = 0.0946286, antiderivative size = 67, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ \frac{125}{64} (1-2 x)^9-\frac{12675}{512} (1-2 x)^8+\frac{28555}{224} (1-2 x)^7-\frac{21439}{64} (1-2 x)^6+\frac{144837}{320} (1-2 x)^5-\frac{65219}{256} (1-2 x)^4 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)^3,x]

[Out]

(-65219*(1 - 2*x)^4)/256 + (144837*(1 - 2*x)^5)/320 - (21439*(1 - 2*x)^6)/64 + (
28555*(1 - 2*x)^7)/224 - (12675*(1 - 2*x)^8)/512 + (125*(1 - 2*x)^9)/64

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - 1000 x^{9} - \frac{3675 x^{8}}{2} + \frac{230 x^{7}}{7} + \frac{3617 x^{6}}{2} + \frac{3279 x^{5}}{5} - \frac{2659 x^{4}}{4} - 375 x^{3} + 108 x + 216 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**3*(2+3*x)**2*(3+5*x)**3,x)

[Out]

-1000*x**9 - 3675*x**8/2 + 230*x**7/7 + 3617*x**6/2 + 3279*x**5/5 - 2659*x**4/4
- 375*x**3 + 108*x + 216*Integral(x, x)

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Mathematica [A]  time = 0.00370956, size = 54, normalized size = 0.81 \[ -1000 x^9-\frac{3675 x^8}{2}+\frac{230 x^7}{7}+\frac{3617 x^6}{2}+\frac{3279 x^5}{5}-\frac{2659 x^4}{4}-375 x^3+108 x^2+108 x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)^3,x]

[Out]

108*x + 108*x^2 - 375*x^3 - (2659*x^4)/4 + (3279*x^5)/5 + (3617*x^6)/2 + (230*x^
7)/7 - (3675*x^8)/2 - 1000*x^9

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Maple [A]  time = 0.002, size = 45, normalized size = 0.7 \[ -1000\,{x}^{9}-{\frac{3675\,{x}^{8}}{2}}+{\frac{230\,{x}^{7}}{7}}+{\frac{3617\,{x}^{6}}{2}}+{\frac{3279\,{x}^{5}}{5}}-{\frac{2659\,{x}^{4}}{4}}-375\,{x}^{3}+108\,{x}^{2}+108\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^3*(2+3*x)^2*(3+5*x)^3,x)

[Out]

-1000*x^9-3675/2*x^8+230/7*x^7+3617/2*x^6+3279/5*x^5-2659/4*x^4-375*x^3+108*x^2+
108*x

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Maxima [A]  time = 1.39608, size = 59, normalized size = 0.88 \[ -1000 \, x^{9} - \frac{3675}{2} \, x^{8} + \frac{230}{7} \, x^{7} + \frac{3617}{2} \, x^{6} + \frac{3279}{5} \, x^{5} - \frac{2659}{4} \, x^{4} - 375 \, x^{3} + 108 \, x^{2} + 108 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(3*x + 2)^2*(2*x - 1)^3,x, algorithm="maxima")

[Out]

-1000*x^9 - 3675/2*x^8 + 230/7*x^7 + 3617/2*x^6 + 3279/5*x^5 - 2659/4*x^4 - 375*
x^3 + 108*x^2 + 108*x

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Fricas [A]  time = 0.178146, size = 1, normalized size = 0.01 \[ -1000 x^{9} - \frac{3675}{2} x^{8} + \frac{230}{7} x^{7} + \frac{3617}{2} x^{6} + \frac{3279}{5} x^{5} - \frac{2659}{4} x^{4} - 375 x^{3} + 108 x^{2} + 108 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(3*x + 2)^2*(2*x - 1)^3,x, algorithm="fricas")

[Out]

-1000*x^9 - 3675/2*x^8 + 230/7*x^7 + 3617/2*x^6 + 3279/5*x^5 - 2659/4*x^4 - 375*
x^3 + 108*x^2 + 108*x

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Sympy [A]  time = 0.096941, size = 51, normalized size = 0.76 \[ - 1000 x^{9} - \frac{3675 x^{8}}{2} + \frac{230 x^{7}}{7} + \frac{3617 x^{6}}{2} + \frac{3279 x^{5}}{5} - \frac{2659 x^{4}}{4} - 375 x^{3} + 108 x^{2} + 108 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**3*(2+3*x)**2*(3+5*x)**3,x)

[Out]

-1000*x**9 - 3675*x**8/2 + 230*x**7/7 + 3617*x**6/2 + 3279*x**5/5 - 2659*x**4/4
- 375*x**3 + 108*x**2 + 108*x

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GIAC/XCAS [A]  time = 0.213984, size = 59, normalized size = 0.88 \[ -1000 \, x^{9} - \frac{3675}{2} \, x^{8} + \frac{230}{7} \, x^{7} + \frac{3617}{2} \, x^{6} + \frac{3279}{5} \, x^{5} - \frac{2659}{4} \, x^{4} - 375 \, x^{3} + 108 \, x^{2} + 108 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(3*x + 2)^2*(2*x - 1)^3,x, algorithm="giac")

[Out]

-1000*x^9 - 3675/2*x^8 + 230/7*x^7 + 3617/2*x^6 + 3279/5*x^5 - 2659/4*x^4 - 375*
x^3 + 108*x^2 + 108*x